You don't say what ISP you are using.
Most ISP's will only allow one connection to the internet from the broadband modem.
The way around this is to install a router or have a pc with 2 network cards and ICS installed.
I live in the UK and use Telewest Broadband. To gain access to the internet the mac address of my network card needs to be registered with Telewest and then it can receive an ip address via DHCP. This might be similar to your setup which is why only the first PC gets internet access.
If you post the details of your ISP, maybe we can get more information to help you solve your problem.